一类有效序列的构造  

Construction of a class of effective sequences

作　　者：陈艳妮[1] 刘琴[1] 薛春梅 张邺[1] CHEN Yanni;LIU Qin;XUE Chunmei;ZHANG Ye(School of Mathematics and statistics,Shaanxi Normal University,Xi an 710119,China)

机构地区：[1]陕西师范大学数学与统计学院,陕西西安710119

出　　处：《西安邮电大学学报》2021年第3期84-89,共6页Journal of Xi’an University of Posts and Telecommunications

基　　金：国家自然科学基金项目(11971283);中央高校基本科研业务费项目(GK 201903008)。

摘　　要：从算子理论的角度分析无限维Kaczmarz算法的收敛性,构造可使Kaczmarz算法保持有效的一类序列。向希尔伯特空间的一组正规正交基中添加一些单位向量,探讨所得新序列的有效性。求解一类与Kaczmarz算法有效性等价的算子方程,给出此类序列有效刻画,进而得到一类有效序列的构造方法。The convergence of infinite dimensional version Kaczmarz algorithm is discussed from the perspective of operator theory.The effectiveness of a class of sequences which is acquired by adding some unit vectors to an orthonormal basis is studied.By solving a class of operator equations related to the efficiency of Kaczmarz algorithm,the effective characterization of this kind of sequences is given,the construction method of such a class of effective sequences is obtained.

关 键 词：Kaczmarz算法 代数重建技术 有效序列 投影 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] O177.1[自动化与计算机技术—计算机科学与技术]